The Commission on Domestic Violence (CODV) of the American Bar Association has published a list of 19 claims about domestic violence in divorce cases, an MediaRADAR.org finds that 17 of the 19 are false.
The ABA propaganda is certainly wrong, but I don't know if there is good data for some issues. For example, what is the incidence of domestic violence in disputed custody cases? Just from my experience sitting in on family court, I would say that most of the cases have a bogus domestic violence accusation. Often the accusation is about some event that took place a couple of years earlier, with no witness, no injury, and no police report. I would bet that most of these accusations are bogus. Disgruntled moms make this stuff up in order to win custody. Often the story is not even plausible. Even when the mom gets caught in a lie, she suffers no penalty for lying.